Relevance is described at s 55 of the Evidence Act 2008,
55. Relevant evidence
(1) The evidence that is relevant in a proceeding is evidence that, if it were accepted, could rationally affect (directly or indirectly) the assessment of the probability of the existence of a fact in issue in the proceeding.
(2) In particular, evidence is not taken to be irrelevant only because it relates only to-
(a) the credibility of a witness; or
(b) the admissibility of other evidence; or
(c) a failure to adduce evidence.
What is a fact in issue will be determined by the trial judge. In R v Middendorp  VSC 147, Byrne J said [at 17]:
17 This is a criminal trial. The accused by pleading not guilty raises the general issue. At common law an accused is incapable of admitting a fact. Pursuant to s 184 of the Evidence Act an accused may admit matters of fact, subject to certain conditions or agree facts pursuant to s 191. Under s 183 of the Criminal Procedure Act an accused may make an admission in response to a notice of pre-trial admissions given by the prosecution under s 182. None of these courses appears to have been taken in this case, so that all factual matters to be proved by the prosecution are technically facts in issue.
It’s notable that relevance relates to facts in issue, not elements of a charge. If evidence was only admissible if it bore on an essential charge element, evidence that would tend to show a motive for a crime could be inadmissible, not in the exercise of discretion but absolutely. Arguably, the motive for a crime goes toward demonstrating both the identity and the intention of the perpetrator, but it won’t do so in every case. A charge can be proven at law without the Crown having proved why the accused person committed the offence (for a tragic example, see R v Guinab  VSC 110.)
If the law was applied the other way, when a husband was charged with his wife’s murder, evidence proving his contemporaneous affair with another woman might not be admissible. That’s not an outcome that common sense would tolerate.
In Plomp v R (1963) 110 CLR 234 that factual scenario arose. It was alleged that the appellant had drowned his wife to be with another woman. He argued on appeal to the High Court that the jury should have been told that the fact that the wife had been drowned would first have to be proved before the evidence of the affair could be considered.
The Court rejected the argument. The admission of the evidence at trial was approved, and didn’t require the murder to be proved before evidence of motive for the crime became relevant [Kitto J at 247, the rest of the Court concurring]:
The argument that to prove a person had a motive for doing an act cannot be relied upon to prove that he did the act was also supported by references to persuasive authority – but again I am unpersuaded. The authorities cited were relied upon in the first place to show that the term corpus delicti relates at most to the commission of a criminal act by somebody and does not cover the commission by an accused person of the criminal act charged against him – that is, here, that [the victim] had not died accidentally but had been killed, but not that the applicant had drowned her. Had the authorities cited not gone beyond this, they would hardly have assisted the applicant’s case, but it was sought to attach this limited meaning to the term corpus delicti as a step towards establishing that it was not until the corpus delicti had been proved that evidence that the applicant had reasons for killing her and had sought to take advantage of her death became material, and some of the authorities cited do give some support to this contention.
The authorities were then referred to. He continued,
Notwithstanding such support as counsel have been able to muster for their submission, I am satisfied that proof of a case cannot be so fragmented. The cause of death, to the exclusion of suicide or accident, is unquestionably part of the corpus delicti, yet proof of this is often inseparably involved with proof that the person who is charged with homicide caused the death. In such a case it could not be maintained that proof of identity must wait upon proof of the corpus delicti. Futhermore, in such a case any evidence to show that an accused person caused the death would be at once evidence of the corpus delicti and an indication of who it was that committed the crime.
Indeed, this is just such a case and any evidence tending to prove that the deceased was drowned by the applicant was evidence against him for all purposes of the case. Such evidence – as will appear in greater detail when I come to the third question – included that there were inducements for his killing his wife; that immediately before her death he spoke of her as dead and introduced another woman as her successor, so, it could be taken, manifesting a disposition to kill her; that immediately after her death he sought to take advantage of her death by attempting to marry the other woman; that he lied about his relationship with the other woman and sought to induce her to do the same; and that he gave various accounts of what happened when the deceased was drowned. It hardly needs to be stated that to prove motive for a crime and no more could never be sufficient evidence upon which to convict anyone and it is to this that it seems to me some of the authorities cited are really directed, but, in a case like this, proof of such matters as I have just indicated does bear upon the probability that the applicant killed the deceased. Such proof was therefore admissable and could be used as evidence both that [the victim] was killed and that it was the applicant who killed her.
To hold otherwise would really involve the absurdity of requiring the jury to be directed that they could not consider the evidence to which I have just referred unless and until they had decided that [the victim] was killed by the applicant because, if she were killed, it must have been by the applicant.
Since relevant evidence relates to facts that are in issue, a carefully crafted concession by the defence can have the effect of rendering otherwise probative prosecution evidence inadmissible. (Heydon J discusses this in the context of similar fact evidence in his dissent in Stubley v Western Australia  HCA 7). A more common example is the concession of the fact of death in a murder trial, saving the need for the trier of fact to hear gruesome details.
I haven’t heard of counsel making the concession ‘my client wished her dead’ for an accused who denied the offence outright but I suppose that, in the right circumstances, it could happen.