The plan sponsor is the employer that establishes and maintains the plan. For a sole proprietor that is you, through your business; for a corporation, the corporation; for a partnership or multi-member LLC, the partnership itself. A partner cannot set up a separate plan for their own share of partnership income.
The sponsor adopts the plan document, makes the contributions and takes the deduction: on Schedule 1 of Form 1040 for a sole proprietor or partner, and on the business's own return for an S or C corporation. It is also answerable for the minimum required contribution every year.
In a one-person plan the owner is the sponsor through their business, and also the trustee and plan administrator. Maxed is none of these. It prepares the documents and filings the sponsor signs.
Which business sponsors the plan matters. Its type decides what counts as pay, when the deadlines fall and how much can be deducted, and other businesses under common ownership may be pulled in through the controlled group rules. See S corporation owners, sole proprietors and single-member LLCs and partners and multi-member LLCs.