Does funding rounds dilute equity or change equity structure?

Dear Searchfunder community,

I reach out to you all asking for orientation on the following. Since the search funds take two funding rounds (One for the search and one for the acquisition of the target company) the question is:

Similarly to funding rounds for Startups, does the search funds' equity structure change (and maybe dilutes ownership) for the investors and entrepreneurs with every funding round?

I'm maybe assuming the funds for the search and the funds for the acquisition are treated as two separate funding rounds. Or it is something that depends entirely on the negotiations between searchers and investors.

As a side note, I'm currently writing my Master thesis and I'm including a fictional acquisition of a nursing home. I will appreciate any help or orientation.

Rodrigo.