I want to expand my property management company. Anyone with any ideas of the most effective way to do this?

Internet, Internet, Internet... You gotta have Google juice.
You need a powerful web presence and you need to own certain keywords. That requires a lot of SEO work or you can pay for ads. Google Ads are OK, but there is a lot of click fraud and you will pay a lot of money.
Social networking, create a Facebook page for your business and promote it. One of my most effective tools right now is Facebook Ads.
Using Facebook Ads you can target people who's profiles contain words like "real estate investor" "real estate investing" . You can also target by location and any number of other factors.
Follow sales of property that fits your management portfolio type, if that is apartments then watch to see when a property sells and use the tax records to send mail to the new owner.
Contact real estate agents who do not manage property and offer them a percentage of the first months rent for referrals.
Follow expired listings on the MLS and send the owners information about your services, tell them that maybe now is not the best time to sell and you can offer them an alternative.
Market out of the box, get some press, offer something unusual to attract attention.
Google, Bing and Yahoo all rank sites differently, getting yourself in the news is a sure way to bump your ratings.
Join groups and associations that relate to your line of work, when you are a member they often link back to you and send you referrals. Check out NARPM, IREM, CCIM and NAA,
Best of luck.

When I was in the office/commercial/industrial real estate management business, I would walk through business parks close to the ones I was managing, estimate how much time would be involved and submit a unsolicited quote to the building owner(s). In CA we could find the owner's names in the tax records or from the escrow department. All of our managers held real estate licenses, so we also quoted leasing vacancies as well as managers. Basically, you will do a lot of legwork and research to submit the quote, that you may or may not be awarded. But, you never know - maybe the owners are considering a change in management companies. Also - network - go to every "open" gatherings at the BBB, real estate offices, Rotary Clubs, etc. The more your name is out in the mix, the better chance you will have of gaining more clients. Good luck - and have fun.

Fastest way is to buy out competitors

I forgot to mention I have not done this myself however a management company that managed a portfolio of investments for one of my clients did this and they went from under 100 properties to over 700 in few years from aquiring other management companies. I was very close to the operations manager was fascinated how they did it.

Word of mouth advertising from satisfied customers of yours is best. Ask them for referrals!