Telstra Corporation Ltd (ASX: TLS) is Australia’s largest telecommunications provider, and its shares pay a big dividend.

For so many years, Telstra ran the network which connected almost every Aussie to a telephone and broadband internet.

Nearly as impressive, since the beginning of 2011 investors in Telstra’s shares have enjoyed a 100% run-up in price and received cash dividends and tax-effective franking credits.

Source: Google Finance

Source: Google Finance

However, some would now argue that Telstra shares have run their race. That the company has now lived out its most profitable days, in command of Australia’s 100-year-old copper cable network, and is quickly losing relevance.

At today’s prices, Telstra’s shares are worth $68 billion combined. The next closest Australian rival is TPG Telecom Ltd (ASX: TPM) at $10.4 billion (which recently bought iiNet), followed by Vocus Communications Limited (ASX: VOC) at $5 billion.

Telstra’s sheer size is a result of its market reach and dominance across business lines like mobiles, fixed internet, pay TV (via its ownership stake in Foxtel) and a number of bolt-on businesses. It also has operations throughout Asia.

However, with the NBN Co slowly taking control of Australia’s lucrative fixed network, competition for services like broadband is growing rapidly. Telstra’s pay-TV arm is also under pressure from the recent arrivals of Netflix, Stan, Fetch and Presto — not to mention proprietary on-demand streaming services.

That leaves mobiles as the jewel in the crown for Telstra. Its extensive and (mostly) reliable network is what gives it pricing power over other providers like Optus and Vodafone.

Is Telstra Corporation Ltd a must-have in retirement portfolios?

All things considered, Telstra has dominated its rivals due to regulatory and competitive advantages. As a result, it’s attracted risk-averse share market investors seeking income.

However, if you plan to invest for its dividend yield — which currently stands at 5.6% fully franked — you must consider the long-term outlook for its business, the risks, and pay a good price.

Personally, I think Telstra shares are a little expensive considering the downside risks, and investors should look for other high-yielding dividend shares to add to their retirement portfolios while we wait for a more compelling price.

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Motley Fool Contributor Owen Raszkiewicz has a financial interest in Vocus Communications. Owen welcomes -- and encourages -- your feedback on Google+, LinkedIn or you can follow him on Twitter @ASXinvest.

The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.